Please anyone tell me how laplace transformation is derived. It transform a funtion into new one. Then what we get? Any example to show how it make a function easy to solve?
A Fourier Transform converts a Steady State Time Domain function/signal to the Frequency Domain.
Basically it integrates [adds up] the energy at differenct frequecies to obtain the signal's spectrum.
It is what a Spectrum Analyzer does.
A variable frequency filter measures the energy at different frequencies
The Laplace Transform [LT] does the same thing but for Transient [non Steady State] signals and can
show the transient response. It is a fundamental tool in Dynamics as both signals and
"black boxes" have a LT and you can just multiply them to get the output response in the Complex Domain.
Then an Inverse Transform produces the output in the Time Domain.